Enfortumab Vedotin and Pembrolizumab With Cystectomy and/or Ureterectomy for Locally Advanced or Metastatic Bladder and Upper Urothelial Tract Cancer, CAST-AI Trial

Inclusion Criteria: * 18 years of age or older at the time of informed consent * Histologically proven urothelial carcinoma \[American Joint Committee on Cancer (AJCC) 2017\] of the bladder (BCa) or upper urothelial tract (UTUC), N+ and/or M+. Initial diagnosis must be within 90 days of planned date for treatment initiation * The following variant histologic subtypes are permitted in any amount * Urothelial with squamous differentiation * Urothelial with sarcomatoid differentiation * Mixed variant histologic subtypes are permitted if urothelial differentiation is predominant (e.g., \< 50% variant histologic subtype) * Willing to undergo cytoreductive cystectomy (CC) or ureterectomy (U) and deemed clinically a surgical candidate (presuming good response) by the attending urologist * Eastern Cooperative Oncology Group (ECOG) performance status grade 0, 1, or 2 * Hemoglobin ≥ 8.0 g/dL (obtained ≤ 28 days prior to registration) * Absolute neutrophil count (ANC) ≥ 1500/mm\^3 (obtained ≤ 28 days prior to registration) * Platelet count ≥ 80,000/mm\^3 (obtained ≤ 28 days prior to registration) * Alanine aminotransferase (ALT) OR aspartate transaminase (AST) ≤ 3.5 x upper limit of normal (ULN) (obtained ≤ 28 days prior to registration) * Total bilirubin ≤ 3 x ULN OR direct bilirubin ≤ 3 x ULN (obtained ≤ 28 days prior to registration) * Estimated glomerular filtration rate ≥ 15 ml/min (obtained ≤ 28 days prior to registration) * Prior systemic chemotherapy for indications other than urothelial cell carcinoma of the bladder is permitted, but interval between this treatment and study enrollment must exceed 24 months * All adverse events associated with any prior surgery must have resolved to CTCAE version 5.0 grade \< 2 prior to registration * Must sign an informed consent form (ICF) indicating that the participant understands the purpose of, and procedures required for, the study and is willing to participate in the study and agree to store samples when applicable * Ability to complete questionnaire(s) by themselves or with assistance * Willingness to provide mandatory blood specimens for correlative research * Willingness to provide tissue specimens for correlative research * Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study) Exclusion Criteria: * The following histologic variants/divergent differentiation are excluded from trial participation: * Presence of urothelial carcinoma with histologic variants comprising \> 50% of histology * Any amount: neuroendocrine, micropapillary, or signet ring cell features * Prior systemic chemotherapy for urothelial cell carcinoma of the bladder at any time (excluding intravesicular therapies) * Known active malignancies (i.e., progressing or requiring treatment change in the last 24 months) other than the disease being treated under study. The only allowed exceptions are: * Skin cancer (non-melanoma or melanoma) that is considered completely cured * Non-invasive cervical cancer treated that is considered completely cured * Breast cancer: * Adequately treated lobular carcinoma in situ or ductal carcinoma in situ considered to have a very low risk of recurrence * Localized prostate cancer (T1c/T2N0M0): * Gleason score 6, treated by either surgery or ablation within the last 24 months or untreated and under active surveillance * Gleason score 3+4 that has been treated (may include surgery or ablation) within the last 24 months and considered to have a very low risk of recurrence (i.e., cT1c or pT2 on prostatectomy specimen) * Received prior systemic chemotherapy or targeted small molecule therapy (excluding hormonal therapy) within 2 years prior to starting study treatment * History of uncontrolled adrenal insufficiency * History of uncontrolled cardiovascular disease including any of the following in the preceding 6 months: unstable angina, myocardial infarction, ventricular fibrillation, Torsades de Pointes, cardiac arrest, or known congestive New York Heart Association class III-IV heart failure, cerebrovascular accident, or transient ischemic attack; pulmonary embolism or other venous thromboembolism * Known active tuberculosis * Is receiving immunosuppression for an allogeneic tissue/solid organ transplant * Participants with an active autoimmune disease requiring systemic treatment. Participants with autoimmune disorders not requiring systemic treatment (eg, skin conditions such as vitiligo or alopecia) or conditions requiring hormonal replacement therapies such as type 1 diabetes mellitus or hypothyroidism are permitted to enroll * Known clinically significant liver disease that precludes participant treatment regimens prescribed on the study (including, but not limited to active viral, alcoholic, or other autoimmune hepatitis, cirrhosis, or inherited liver disease) * Known human immunodeficiency virus (HIV) infection, unless the participant has been on a stable antiretroviral therapy regimen for the last 6 months or more and has had no opportunistic infections and a CD4 count of \> 350 in the last 6 months * Known active hepatitis B or C infection \[however, participants with history of hepatitis C infection but normal hepatitis C virus polymerase chain reaction test and participants with hepatitis B with positive hepatitis B surface antigen (HBsAg) antibody are allowed\] * Known urinary tract infection (UTI), defined as a symptomatic infection with a positive urine culture with a bacterial count of ≥ 10\^5 colony forming units (CFU)/mL in urine voided from women, or \> 104 CFU/mL in urine voided from men, or in straight catheter urine from women. Symptoms may include dysuria, urgency, frequency, and/or systemic symptoms such as fever, chills, elevated white blood cell, and/or abdominal/flank pain. Participants free from symptoms for 7 days with no culture evidence of ≥ 10\^5 CFUs may be eligible * Known active, uncontrolled urogenital bacterial, viral or fungal infections, including UTI. Skin/nail fungal infections are not exclusionary. Participants with active shingles (varicella zoster infection) will be excluded from the study * Evidence of interstitial lung disease or active non-infectious pneumonitis * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, unstable angina pectoris, or psychiatric illness/social situations that would limit compliance with study requirements * Participants who have had a history of acute diverticulitis, intra-abdominal abscess, gastrointestinal obstruction and abdominal carcinomatosis which are known risk factors for bowel perforation * Known history of impaired wound healing capacity defined as skin/decubitus ulcers, chronic leg ulcers, known gastric ulcers, or unhealed incisions * Pelvic radiotherapy administered at any time * Received a live virus vaccine within 30 days of planned start of study treatment * Active autoimmune disease that has required systemic treatment in the past 2 years * Active infection requiring systemic intravenous therapy within 30 days prior to planned treatment initiation * Prior treatment with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CD137, or anti-cytotoxic T-lymphocyte antigen-4 (CTLA-4) antibody, or any other antibody or drug specifically targeting T-cell co-stimulation or checkpoint pathways * Participants with a history of grade ≥ 3 toxic effects when using anti-tumor necrosis factor (TNF) or anti-interleukin (IL)-6 agents are excluded * Participants still recovering from toxicity of prior anticancer therapy which was received more than 24 months prior to enrollment (except toxicities which are not clinically significant such as alopecia, skin discoloration) * Participants who require immunosuppressive medications including but not limited to systemic corticosteroid at doses \> 10 mg/day of prednisone or its equivalence, methotrexate, cyclosporine, azathioprine, and TNF alpha blockers. Use of immunosuppressive medications for the management of immune related adverse events, infusion related reactions, or in participants with contrast allergies is acceptable. Use of inhaled, topical, and intranasal corticosteroids are permitted * Participants with a history of allergy to protein-based therapies and participants with a history of any significant drug allergy (such as anaphylaxis, hepatotoxicity, or immune mediated thrombocytopenia or anemia) are excluded * Currently participating or has participated in a study of an investigational agent and received study therapy or investigational device within 4 weeks prior to enrollment * Participants who have not recovered from the effects of major surgery or significant traumatic injury at least 14 days before registration \[transurethral resection of bladder tumor (TURBT) is not considered major surgery\]. Note: Participants with planned surgical procedures to be conducted under local anesthesia may participate * Any of the following because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown * Pregnant persons * Nursing persons * Persons of childbearing potential or able to father a child who are unwilling to employ adequate contraception * Any condition for which, in the opinion of the Investigator, participation would not be in the best interest of the participants (eg, compromise the well-being) or that could prevent, limit, or confound the protocol-specified assessments * The participant is unable to comply with the requirements of this protocol, including any factors that are likely to affect the participant's return for scheduled visits and follow-up